\section{Goals and Outcomes}

% GOAL PARAGRAPH
This research develops autonomous hybrid control systems with mathematical guarantees of safe and correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
% Known information
Today's nuclear plants depend on human operators who control them through extensive training, following detailed written procedures and strict regulatory requirements while switching between control modes based on plant conditions and procedural guidance.
% Gap
This reliance on human operators prevents autonomous control and creates a fundamental economic challenge for next-generation reactor designs: per-megawatt staffing costs for small modular reactors far exceed those of conventional plants, threatening their economic viability. Autonomous control systems could manage complex operational sequences without constant human supervision—but only if they provide assurance equal to or exceeding that of human operators.

% APPROACH PARAGRAPH Solution
This research combines formal methods with control theory to produce hybrid control systems correct by construction.
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods generate provably correct switching logic from written requirements, but they fail when continuous dynamics govern transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. Both approaches must work together to achieve end-to-end correctness.
% Hypothesis
This approach closes the gap through two steps. First, it synthesizes discrete mode transitions directly from written operating procedures. Second, it verifies continuous behavior between transitions. Operating procedures formalize into logical specifications that constrain continuous dynamics. The result: autonomous controllers provably free from design defects. 

The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring solutions align with practical implementation
requirements.

% OUTCOMES PARAGRAPHS
This approach produces three concrete outcomes:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Translate written procedures into verified control logic.}
    % Strategy
    A methodology converts existing written operating procedures into formal
    specifications. Reactive synthesis tools then automatically generate
    discrete control logic from these specifications. Structured intermediate
    representations bridge natural language procedures and mathematical logic.
    % Outcome
    Control system engineers generate verified mode-switching controllers
    directly from regulatory procedures without formal methods expertise,
    lowering the barrier to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textbf{Verify continuous control behavior across mode transitions.}
    % Strategy
    Methods for analyzing continuous control modes verify they satisfy
    discrete transition requirements. Classical control theory handles linear
    systems. Reachability analysis handles nonlinear dynamics. Both verify that
    each continuous mode reaches its intended transitions safely.
    % Outcome
    Engineers design continuous controllers using standard practices. Formal correctness guarantees remain intact. Mode transitions occur safely and at the correct times—provably.

    % OUTCOME 3  Title
  \item \textbf{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    This methodology applies to autonomous nuclear reactor startup procedures,
    demonstrating on a small modular reactor simulation using industry-standard
    control hardware. The demonstration proves correctness across multiple
    coordinated control modes from cold shutdown through criticality to power operation.
    % Outcome
    Autonomous hybrid control becomes realizable in the nuclear industry with
    current equipment, establishing a path toward reduced operator staffing
    while maintaining safety.

\end{enumerate}

% IMPACT PARAGRAPH Innovation
These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.

\textbf{What makes this research new?} This work unifies discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems—no existing methodology achieves this. The key innovation: treating discrete specifications as contracts that continuous controllers must satisfy, allowing each layer to verify independently while guaranteeing correct composition. Formal methods verify discrete logic. Control theory verifies continuous dynamics. No existing methodology bridges both with compositional guarantees. Section 2 examines why prior work has not achieved this integration. Section 3 details how this integration will be accomplished.

% Outcome Impact
If successful, control engineers create autonomous controllers from
existing procedures with mathematical proofs of correct behavior. High-assurance
autonomous control becomes practical for safety-critical applications.
% Impact/Pay-off
This capability is essential for the economic viability of next-generation
nuclear power. Small modular reactors offer a promising solution to growing
energy demands, but their success depends on reducing per-megawatt operating
costs through increased autonomy. This research provides the tools to
achieve that autonomy while maintaining the exceptional safety record the
nuclear industry requires.

These three outcomes establish a complete methodology from regulatory documents to deployed systems. This proposal follows the Heilmeier Catechism, with each section explicitly answering its assigned questions. Each section begins by stating its Heilmeier questions and ends by summarizing its answers, ensuring both local clarity and global coherence:
\begin{itemize}
  \item \textbf{Section 2 (State of the Art):} What has been done? What are the limits of current practice?
  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed?
  \item \textbf{Section 4 (Metrics for Success):} How do we measure success?
  \item \textbf{Section 5 (Risks and Contingencies):} What could prevent success?
  \item \textbf{Section 6 (Broader Impacts):} Who cares? Why now? What difference will it make?
  \item \textbf{Section 8 (Schedule):} How long will it take?
\end{itemize}